In Exercises 1–12, find each absolute value.
-|-2/5|
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1
Identify the expression inside the absolute value: .
Recall that the absolute value of a number is its distance from zero on the number line, which is always non-negative.
Remove the negative sign from the expression inside the absolute value, as absolute value makes it positive.
The absolute value of is .
Thus, the expression becomes .
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by two vertical bars surrounding the number, such as |x|. For any real number x, the absolute value is defined as |x| = x if x is greater than or equal to zero, and |x| = -x if x is less than zero.
Negative numbers are values less than zero, represented with a minus sign (-). In the context of absolute value, when calculating the absolute value of a negative number, the result is the positive counterpart of that number. For example, |-2/5| equals 2/5, as the absolute value function converts negative inputs to positive outputs.
Fractions represent a part of a whole and are expressed as a ratio of two integers, where the numerator is the top number and the denominator is the bottom number. In the case of -2/5, the negative sign indicates that the value is below zero. Understanding how to manipulate and interpret fractions is essential for accurately calculating their absolute values.